Speaker: Sergey Kitaev, University of Strathclyde, UK

Inviter: 陈绍示（中国科学院数学机械化重点实验室）

Title: Naturally labelled posets and a hierarchy related to interval orders

Language: Chinese

Time & Venue: 2025.03.13 10:00-11:30 思源楼525

Abstract: A partially ordered set (poset) (P,<_P) is naturally labelled by numbers in {1,2,...,n} if x <_P y implies x<y. Naturally labelled posets are in one-to-one correspondence with certain lower triangular binary matrices called poset matrices.

By restricting naturally labelled posets – such as considering (2+2)-free, k-free, (3+1)-free, N-free, and similar classes of posets – we obtain combinatorial objects that fit nicely into a hierarchy related to interval orders. This hierarchy includes, for example, Fishburn matrices, factorial posets, ascent sequences, pattern-avoiding permutations, and many other structures. In particular, it turns out that (2+2,3)-free naturally labelled posets are in one-to-one correspondence with permutations avoiding the vincular pattern 12-34. In my presentation, I will introduce these objects and discuss the hierarchy, along with open (embedding) problems. This is joint work with David Bevan and Gi-Sang Cheon.